Fourier Coefficients of a Class of Eta Quotients of Weight 12 with Level 12

Recently, Williams and then Yao, Xia and Jin discovered explicit formulas for the coefficients of the Fourier series expansions of a class of eta quotients. Williams expressed all coefficients of 126 eta quotients in terms of σ(n),σ(n/2),σ(n/3) and σ(n/6) and Yao, Xia and Jin, following the method of proof of Williams, expressed only even coefficients of 104 eta quotients in terms of σ3(n),σ3(n/2),σ3(n/3) and σ3(n/6). Here, we will express the even Fourier coefficients of 2 eta quotients i.e., the Fourier coefficients of the sum, f(q)+f(-q), of 2 eta quotients in terms of σ5(n),σ5(n/2),σ5(n/3),σ5(n/4),σ5(n/6),σ5(n/12),σ11(n),σ11(n/2), σ11(n/3),σ11(n/4),σ11(n/6),σ11(n/12),τ(n)(tau function),τ(n/2),τ(n/3),τ(n/4),τ(n/6),τ(n/12) and the odd Fourier coefficients of 393 eta quotients in terms of σ5(n),σ5(n/2),σ5(n/3),σ5(n/4),σ5(n/6),σ5(n/12),σ11(n),σ11(n/2), σ11(n/3),σ11(n/4),σ11(n/6),σ11(n/12),τ(n),τ(n/2),τ(n/3),τ(n/4),τ(n/6),τ(n/12) and f13,...,f19